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Question Number 18827 by aplus last updated on 30/Jul/17

Commented by aplus last updated on 30/Jul/17

$$\mathrm{help}\mathrm{guys}$$

Commented by mrW1 last updated on 30/Jul/17

$$\mathrm{no}\mathrm{solution}$$

Commented by dioph last updated on 31/Jul/17

$$\mathrm{if}\mathrm{both}x\mathrm{and}y\mathrm{are}>1:$$$$x^x>x,y^y>y\Rightarrow x^x+y^y>x+y$$$$\Rightarrow 6>35,\mathrm{absurd}$$$$\mathrm{if}\mathrm{exactly}\mathrm{one}\mathrm{from}x\mathrm{or}y\mathrm{is}<1,$$$$\mathrm{say}x<1:$$$$x+y=35\Rightarrow y>34\Rightarrow y^y>{34}^{34}$$$$\Rightarrow x^x+y^y>6,\mathrm{absurd}$$$$\mathrm{if}\mathrm{both}x\mathrm{and}y\mathrm{are}<1:$$$$x+y<2<35,\mathrm{absurd}$$

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